Angular displacement is usually express in units ow l-,ccru6 )jnf

  Angular velocity is exp4swvj, ezqv-f ;0cnv 3ressed in units of

  Angular acceleration iwthlg8x81 fm 3s expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a cjd1kr mww 65z4onstant rate. The boy is near the outer edge, and the girl is closer to the center. dwk146jrmwz5 Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constar, i)y-w *wkr-qc cfkgr 6*yh:nt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular igcy- c-r*f*y6qr wkr w)kh,: speed?

  A boy and a girl are riding on a merry-go-round which is turning adwb6*n/u otrt-q -y8c nkp2)q t a constant rate. The boy is near the outer edge, and the girl is closert28dqrknpu6o)w - *n yt/-q cb to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which i s6:c m5awhqe y:nsd- ,vwhjg;b5o z9,s turning at a constant rate. The boy is near the outer edge, while the girl is closer to the956 ;qwm, ndb-,ac5w syg:j:evohs hz center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a con2 v4 yk;fe a))i6*qzt/tui rdastant rate. The boyt2)t)rv/;6 ke*au fi z4qdaiy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of apptl cyu+)n5u kxz6 +9yad09the following is an accurate statemenk+ xyu99n+p0zcdyaau ) 56tl pt?

  Rolling without slipping dependse+qefk 8bb+.o on

  Two equal forces are applied to a door. The first force is applied at the midpr8 usxp95oc u*a:xg5c, id1 ,f 2kn7 lvpxhlh7oi7iscp8pxk o*hxn9 v,2f1udlhc5arlgu7x,5 : nt of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appl4u kwd 3rbiz u9gqi;,nsq- p.02kmu 2died to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts thqr22g nbiw 9dmk s.- pu;k03qzi,ud4ue greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. ,/ .-eadq7i v1ub m6grmyw,j zThe first force is tw,q a,zbju6 riymwm-v1 d7.e/ gice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to m4;c)2m n cizm( iwr5uveasure an object's resistance to changes in rotaticzv m nu)2m5wr;i(i4con?

  Consider two uniform solid spheres when ;g8+na+l nqore both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to ta on8l;ngq++nhat of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice thegb3 yvyze9hspf705t vo )2n4n radius of the other. The ratio of the larger sphere's moment of inertia to that ot 2n 3nbzgv yv)4sfe7y p059ohf the smaller sphere is

  Consider two uniform som8ft mhb )5v 1r4j:zxolid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of z8r54t bmohjmf1:)xv inertia is

  A uniform solid sphere has mass M and3pl8/5wbuvz+ )pu( irihy4ao radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inp hou45(/8y3r ) wuipvibzal+ertia about a central axis?

  If a constant net torque is applied to an object, that object 0tukt527bcaxcd :a yz;2l -zklhga 9. will

  The moment of inertia of a solid cylinder about its axis 5 jyzr ,3 60q;wetnkbf4cv/ kx+xbj)wis given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 13hhy t/ox3:s5ztq6,wil - vtv m*8qvnl-qy3 w50 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to t/ltv:yn3-qwhm 6iwt hv5q* l,vs33ozytq x-8he total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without s::ymg)u qi ax-.clo6slipping down an inclined planoy.6 g-i :qmusacx)l :e starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and2 vy 8s*rr5kuh /zz/6 qex.mvi radius R rolls without slipping down an inclined plane s6zx/vr8 /q5.ieskm2* rhvuzytarting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles c+f ::za-my 9ifscux3ehanges when a net external force acts ::ims+ fec9a3u -fx yzon the system." This statement is

  In what circumstances can the angular velocity of system of partidcl0q/sr ,akab x,;n1cles change without any change in the system's angular momentuax1,, ns/cd;0albrqk m?

  The Earth orbits the Sun in an ei xy,(x gw.fk21 xzuc6lliptical orbit. Ignore any friction which may be present. What happens over time to thex., x6gfw(2c 1kzxiuy Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical oup(wyxv;sxd5 refvq e4 v9vn,/ ;,*uv rbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed,/uxxwvs 4yv fvnvp ;;r*,queve9(d 5 of the Earth about the Sun?

  An ice skater perfor +fiwc s6 l;)alqbq)2mms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momen+qbf); sla2 )6l imqcwtum about the axis of rotation?

  An ice skater performz 7 mcfzoosk) ijs,3le2fm7t y+k 2u(q;p3ii /s a pirouette (a fast spin) by pulling in his outstretched armfi+ tq2 im( 2c3l;u smzik3pso/,o z7ky)je7 fs close to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a piro-9kswr yc*(o ,k,ippk uette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his momentscw,p,yr i * kkk-9(po of inertia about the axis of rotation?

State the law of conservation of angu qgxmm;je.f)fu4* af0lar momentum.

  What arc length does the Earth travel in a three month period inwl6r*q4dri* ve, t8(d;t apjy9kmqw a)jr .1z its nearly circulaw8z6 )amrqpelqdr 1**j,.jttd4k 9 wy (vr;a ir orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 5j wdeazn2dm )3)1g oen-pi 1h+)zzk um. What distance does the tip of the second hand sweep through in 3 minutes3 2) zhwagnu 5dnzikjmee1-o)d1)p +z and 45 seconds?

  How many rad/s is 25 revolutions per minutep0je;zlo xnkna2s,h/q* q x .1 equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutionrth6 d i6h)mv;s in 4.0 s. What is the frequency of the wheel's rotat)i;m 6hrtvd h6ion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. wv1hi v)rpxr35v03 rlkf u.2 aThe period of its xr3a1vvrhp3 0 lkr) iv u2fw5.rotation is

  A phonograph record rotates at 45 rpm. Through tpbioj5m*w m:d, mh 1v o;si,6what angle does it turn in 0.20 ,sm v j: 5iwodpt6b mhmo1;i*,s?

  A wheel of diameter 26 cm turns at 1500 rpm. 3/iqzbuk9qrm e.b7b/b n1 z y1 How far will a point on the outer rim move in 2.1 s7byu z/9z e1q mb3n/.1qbbi rk?

  A bicycle wheel rotates uniformly throubz;7,zu-zn yrd l/0c ogh 2.0 revolutions in 4.0 s. What is the average angular speed olc;y z z0b/z-,7uro dnf the wheel?

  A bicycle wheel rotates uniformly through5 dps r5m/9ru z3pndf, 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center ofz/d5 5d ufsr,9r pnmp3 the wheel?

  A cable car at a ski resort carr* d;)sq /cbzrries skiers a distance of 6.8 km. The cable which moves the car is driven by a r/;d cqrbz*)s pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant an;f 7v;pe mdadlwn g4n86wj*p(gular speed of 2.0 rad/s. What is the linear speep7a d n4dvwf jg;lm n*(ep;8w6d of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. Iih*59h9:ltmfh yr c yj wpy8+2f the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of theyjrc5+* hi28l ywpf9hyh9 :mt end of the cord?

  A wheel of radius 1.0 m6l*+g g5k awhw;ap4 aj is rotating with a constant angular speed of 2.0 rad/s. What *wagj;p4la gk6 a5wh+is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceler r loj3 * ryd3d:(j;*akcjtz 4vul*cx o/d+yk5ation of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is my/xvcr( c ku5d :lao tj3l +3j;yo4rd*jdz*k* oving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statioowk79p g-4slkn27sv k n (r = 1000 m) rotate to prodk 2n7sw4l7 gpv9k- skouce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fla9yb4 5xey:uv qt circular curve of radius 50 m with a speed of 20 m/s. The u5qe4:y x y9bvmaximum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a sp5s57t0 dw(sr e,ubl nseed of 20 m/s. The maximum centripetal forc,ns rwts(s75ub 5l 0ede (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is whirled aroun4e hbnl :h93pyd in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear spe:4p hbhn39 elyed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m do+i en pvki0/u8i8* vypx- tr5nwn a l-up5yxi rk */nn pi88v+eiv0tane at 4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates with a constant angular accelo,v29 : -bol fj3fbheqeration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a constant angulari (yei4dia3 y; acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radius automobi x kd/t::1/ept+lfz9dbecn,c le tire rotate after starting from rest and accelerating at a constant angular +/n:, bt et /lfp1ecd 9kzxc:dacceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerat9frkpi/(kr r0v ryuj q2d 6b-:ion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating atd9u. f mwxq-,g 20 rad/s decelerates with a constant angular acceleration of mgqu d9,fw .x-$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while cjlz hyls+lx21 / ;;ktturning through 2.0 revolutions. What is the average angular acceleration of t lxkj+2zc ; 1h/l;sltyhe wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s m+kxbphj ,.uk /h kfwmpnw35f;iv5 -6to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comffhx6knm hpkp/k5,-im.b + v ;uj53wwing to rest?

  A wheel of diameter o d:owieb) (0jmf 68.0 cm slows down uniformly from 8.40 m/s to rest over a dista:wejd0(bm)oi nce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to env yh(8-d dfr9qb4,b rest over a distance of 115 m. How long does it take for the wheel to come to th,ebdbry h(v98- f4qdn e stop?

  A centrifuge in a medical(mhe2xdq sfvho32j8:ir w1 6q laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 timdh ej23q6f(xsm:h o 8w12vrqies at a constant angular acceleration before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tighte7sh -9hn2(ld i+sxirjning to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to thhsid2+-7 xsjr9ln h( ie wrench?

  The bolts on a car wheel require tiv+nqfp3k09p sw )05l7kn g5ygz f(t gughtening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force regl(n573+ff0 p )w0kq9s tknvguyg p5z quired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertgg a1f7u7cf* s3 ebkk0ia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at thelz ./kyhhl x-9 origin, mass 2m is at x = a, and, mass 3m is atl 9 xzkh.-lh/y x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionl3pz/7teh ifa(v mr70 b f;+dsiw m,(guess axis thought the center O. A rope wrapped around the o; wbu(7vsp+i(mf gdfth ,3mz/ re07 aiuter radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mal./qkos: gg:*04xv yl r-bksf6urzliw2 en .*ss 10 kg is pivoted about a frictionless axis thought the center Oolkkzbi4: l-.06g .ruvy/2nwsr exqflg* *s: . A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially;r,u 4 7xbsl )fpgx:gi held in the horizontal position, and then released as the free end is allowed to fall. What is the angular ac4i),rp:sbugg; l7 xx fceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to 5zne4x j/z dr3be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially d4zejx 53 /rnzto a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frqyd+p l/(eds8ictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What i d(splye+ q8d/s the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fricta9 u3vz gtr9i*ionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accel rtug 9a3vi*z9eration of the mass?

  A rotating flywheel can be used to store energyll+62mvqitk(nly(4-bn c n*p . If it is required to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of(2 ky xma1u6mm*i.ejb inertia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and r l4yyi j6)0vkr4z 0plradius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?k z4 4lr)iv00yrj6ypl

  A solid sphere of mass i uxmsr;alut:x5:9j 81.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comi sutxx:89ar ;jmu 5l:ing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releajwtvex-* e:fel z 33+ kewv//csed from rest and allowed to roll dwj twzcvlv/k3e+*ee fe 3/x-: own an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippyzh; 6g).b f6rniyc/ping down a 35e incline that is66.yzcp yrf;nbh/ g )i 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum chz ud,(m rmo614:ysll qanges by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment of inertiaj7i)v8 tm;gak of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00pi,:n7kcq yt+ rad/s with arms extended has a moment of inertiayiqkc:7 n,+t p of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?